His relationship with his old friends in the village would become more complex. They might see him as someone who has moved into a different social class. For example, Sasuke might view him with suspicion or envy, thinking Naruto has abandoned their shared past as shinobi.
His relationship with his old friends would definitely change. He would have less time for casual training and hanging out. For example, his bond with Sasuke might become more formal as Naruto is now in a position of power. But they would still respect each other's roles.
With his new status and appearance, Naruto's relationship with his family would also change. His relationship with Hinata might face new challenges as he has to balance his duties as Daimyo with his family life. His children would grow up in a different environment, with Naruto being a figure of political power. And his relationship with the older generation, like Kakashi, would shift as they now have to respect him as a leader.
His relationships with his friends in Konoha would become more complicated. They might be suspicious of Medusa and worry about Naruto being influenced by her. But at the same time, Naruto could try to convince them that Medusa is not all bad. With his enemies, they might be more afraid of him because of his connection to Medusa.
His relationship with Hinata would be completely different. Instead of a potential love interest, she'd be his sister. His relationship with Neji might also change. Neji might be less hostile towards Naruto as they'd be part of the same family. Naruto would also have a new relationship with Hiashi as his adoptive father, and he'd have to follow Hiashi's rules and guidance.
His relationships with his old friends would be different. Some of his friends might be distrustful at first. For example, Sasuke might see Naruto's new situation as a betrayal of their shared experiences. However, over time, if Naruto could prove that he was still the same person at heart, they might reconcile. With Orochimaru as his adopted father, Naruto would also form new relationships within Orochimaru's circle. He could meet some of Orochimaru's former subordinates who might now be on a more positive path, and they could become comrades or even friends.
His character might become more refined. Growing up in a Daimyo's family would expose him to different values and cultures. He could become more diplomatic and less brash.
His relationships would change a great deal. He'd probably form a father - son type of bond with the Raikage. With the other Cloud ninjas, he'd start as an outsider but gradually earn their respect through his skills and determination. His relationship with his friends in Konoha might become more complex as he now has a new allegiance to the Hidden Cloud.
Naruto's relationship with the Hokage would also be altered. He might not have the same drive to be recognized by the Hokage in the same way. Instead, he would be more concerned with making Inoichi proud and living up to the Yamanaka clan's expectations. And his friendships within the Yamanaka clan, like with Ino, could be really deep. They might train together and develop new jutsu as a team, which is different from his relationships in the original story.
Well, Naruto being adopted by the Fire Daimyo might lead to him having a more luxurious lifestyle. He could have access to the best tutors, learn about different cultures and history from all over the Fire Country. However, he might also face new enemies within the political circles who see him as a threat to their own power.
His relationship with Sasuke might become more complex. Sasuke, who has always been somewhat cold - natured, could be either drawn to Naruto's fiery energy or feel threatened by it. Sakura might be more cautious around him at first, afraid of getting burned. But as she realizes Naruto's good heart beneath the fire, she could become more protective of him.